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- W2203699599 abstract "We consider encoding problems for range queries on arrays. In these problems the goal is to store a structure capable of recovering the answer to all queries that occupies the information theoretic minimum space possible, to within lower order terms. As input, we are given an array $$A[1..n]$$ , and a fixed parameter $$k in [1,n]$$ . A range top- $$k$$ query on an arbitrary range $$[i,j] subseteq [1,n]$$ asks us to return the ordered set of indices $${ell _1, ..., ell _{k}}$$ such that $$A[ell _m]$$ is the $$m$$ -th largest element in $$A[i..j]$$ , for $$1 le m le k$$ . A range selection query for an arbitrary range $$[i,j] subseteq [1,n]$$ and query parameter $$k' in [1,k]$$ asks us to return the index of the $$k'$$ -th largest element in $$A[i..j]$$ . We completely resolve the space complexity of both of these heavily studied problems—to within lower order terms—for all $$k = o(n)$$ . Previously, the constant factor in the space complexity was known only for $$k=1$$ . We also resolve the space complexity of another problem, that we call range min-max, in which the goal is to return the indices of both the minimum and maximum elements in a range." @default.
- W2203699599 created "2016-06-24" @default.
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- W2203699599 date "2015-01-01" @default.
- W2203699599 modified "2023-10-17" @default.
- W2203699599 title "Optimal Encodings for Range Top-$$k$$, Selection, and Min-Max" @default.
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- W2203699599 doi "https://doi.org/10.1007/978-3-662-47672-7_48" @default.
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